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40 2 INDUST RIAL AND ENGINEERISG CHEJI IST RY 1-01. 17, S o . 4

explosive mixture, P / T is constant and the expression issimpler. For maximum dP/dt from Equation 15,

d ( . - "= I3

Conclusion

Becau se rat e of rise of pressu re and ra te of combustionhave been confused with rate of reaction, it has generallybeen assumed that an increase in initial temperature mustincrease the rate of combustion or of rise of. pressure of a

gaseous explosion. Th e experimental work reported in this

paper shows that an increase in initial temperature above adefinite critical value decreases the rate of rise of pressure ofa gaseous explosion. Th e theoretic al considerations pre-sented show that the existence of a critical initial tempera-tur e is to be expected from our knowledge of gases an dgaseous reactions.

b

f B f / B 2 + 4 b B / c

2T =

As b, C, and B are positive an d finite, the initial tempera ture(T) as a real positive value for the maximum rate of rise of

pressure for a given dens ity of an explosive mixture.

The Measurement of the Temperature of aFlowing Gas'

By R. T. Haslam and E. L. Chappell

MASSACLW6ETTS INSTITWTa O F TECENOLOOY,CAMBRIDGP,MASS

The various methods in use for eliminating errors in

temperature measurements of flowing gases are discussed.

These methods are (1 ) protecting thermometer or pyrom-

eter couple with a polished meta l shield of low radiating

power, (2) the use of a thermocouple of very small diameter,

(3) the use of a series of thermocouples of varying diam-

eters and extrapolating the apparent temperature-diam-

eter of couple curve to zero diameter of couple, and (4 )reducing radiation from the thermocouple by the use

of a heat insulating shield or sleeve.

A new method of gas temperature measurement is dis-

cussed which employs a high gas velocity past the thermo-

couple to bring it to as near the true gas temperature aspossible.

TE accu rate measurement of the te mp eratu re of a flow-

ing gas is more complicated than the measurement ofthe tem per atu re of a solid or a liquid. A thermocouple

or thermom eter is ordinarily inserted in the gas and the tem-perature of this device taken as the true gas temperature.However, such a thermometer or thermocouple reading maybe seriously in error since the flow of h eat b y rad iation b etweenthe surrounding solids and the thermocouple affects the ap-parent gas temperature.

The tremend ous effect of radiation ma y be illustrated bythe following dat a (Table I) taken from work describc 1 later .Air a t a known velocity was blown through a sho rt length

of red hot pipe in the center of which mas placed a thermo-couple.

Table I

Gas velocityTemperature of pipe surfaceTru e temperature of air a t coupleApparent temperature (couple reading)

6.0 feet per second1350' F.270' F.890' F.

In th is case the thermocouple indicated a temp erature 620" F.higher than the true gas temperature and only 460" F. lowertha n the temperature of the surrounding pipe walls.A flowing gas, as in recuperators, blast furnace stoves,

stacks, boiler settings, or furnaces, may be at a tbnpera-ture hundreds of degrees from that of its surroundings, andwhen such a temperature difference exists a large error is

1 Presented before t h e Section of Gas and Fuel Chemistry at th e 68th

Meeting of the American Chemical Society, Ithaca, N. Y., September 8 t o 13,

1924.

A method of calculation is developed whereby the equa-

tion

is made more valuable by the use of the following equation

for the value of

V0.67+ 0.09logD

D .0, = 0.51 T,,,0.4

A summary of the advantages and disadvantages of all

these methods is given in Table VIII, while the error in-

volved in the use of these methods is illustrated by ex-

amples in Table IX .

possible. For exam ple? a hand book 2 mentions a n engineer'sreport on a boiler plant in which a flue gas temperature of386" F. an d steam pressure of 162 pounds were given. As371" F. corresponds to the pressure of 162 pounds, it wasindicated th at the flue gases were only 15 degrees hotter t ha nthe water in the tubes. Investigation showed th at this gastemperature had been measured by a thermometer placedamon g the boiler tubes, which really measured the tu be tem -perature, the gases probably being 200 to 300 degrees hotte r.

It may be noted that boiler plant heat balances generallyaccount for only 92 to 97 per cent of the heat . In many casesthis "unaccounted for" heat is carried out the stack by thegases whose tem perature was rea d too low by an improperlyexposed thermom eter.

It is necessary to recognize that a the rmom eter or thermo-couple measurem ent of a gas tem per atu reis asmu ch influencedby the tem perature of the surroundings a s by t ha t of th e gas it-self, and special precautions and methods must be consideredfor the measurement of the temperature of gas streams. Itis the object of this paper to summ arize some of these meth odsan d to suggest means for the tr ue measurem ent of high gastemperatures.

Factors Determining Reading of Thermometers orThermocouples

Th e tem per atu re of a therm ocouple in a gas will always liebetween the temperatures of the surroundings and of the gas

* H. S. . W.- Cochrane Co., "Finding a nd Stopping Waste in Modern

Boiler Rooms,"Vol. 11, 1921.

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April, 1925 ISDCSTRIAL B S D ENGINEERING CHE?IIISTRY 403

1200

itself. Th is thermocoup le reading represents an equilibrium,the flow of heat by conduction between the gas and thermo-couple having become equal to the flow of h eat by radia tionbetween the thermocouple a nd surroundings.

CoxDUcTIoN-consider a thermocouple placed in a ho t gasflowing through a cold pipe. Th e thermocouple in the gasstream will be heated by conduction from the gas and at a

rate prop ortional to the tem peratu re difference.

I I I I I

r:

where Q = B. t. u. from gas to thermocouple per hour0

T, = gas temperature, ’F. Abs.T , = couple temperature, O F. Abs.A = area of couple, square feethe = coefficient of heat transfer

Th e coefficient of h ea t trans fer, expressed in English uni ts,is the number of B. t. u. w hich will flow in an hour between agas and solid when th e area of c onta ct is 1 square foot and thetem perat ure difference is 1’ F. Th is coefficient depends u ponseveral factors , such as temp eratu re, sha pe of solid surface,the nature of the gas, and its velocity.

RADIATION-The couple will becom e ho tte r tha n the wallsand will radiate heat to them . In accordance with theStefan-Boltzman law, this radiation is proportional to thefourth power of th e absolu te tempera ture and t he ne t flow ofheat to the wall by radiat ion f rom the thermometer or ther-mocouple m ay be expressed by the e quation:

where Q = B. t. u. per hour from thermocouple to walleA = area of couple, square feetTc = couple temperature, O F. Abs. (= F.S

T , = wall temperature,’ F. Abs./100p = black body coefficient of couple

, 460)

When th e loss of heat from th e couple by radiation becomes

equal to the gain by conduction the reading will be consta nt.This equilibrium is shown mathematically by equatingEquations 1a n d 2.

g = h , A (Tg- c) p O . l 6 2 AeThe true gas temperature, To ,may be calculated from the

observed couple reading, To,f all the other factors in thisequation can be determined; or, when the possibility of thiserror is recognized, special conditions may be arranged tomake calculated corrections unnecessary. This usually in-volves either the reduction of the flow of he at b y radia tion be-tween thermometer an d walls , or a stim ulati on of the rat eof heat flow by conduction between thermometer and gas.

GASEOUS ADIATION-If th er m al rad iat ion from the gasestakes place it must be considered as a factor influencing the

thermom eter reading. Radiation from gases has not beenthoroughly s tudied, bu t i t seems probable tha t gases radiateap pr eci ab l y o nl y d u ri ng ch em ical r e a ~ t i o n . ~ , ~4ir a t tem-peratures t ha t can be measured by a thermocouple is not dis-sociated and does not appreciably absorb radiant energy, sowe m ay safely assume t ha t radiation from it is negligible.Radiation from flames,6 hough not ye t subject to mathe mati-cal expression, is sufficiently great to make the readings of athermocouple d irectly exposed to flames erratic a nd uncertain.The l atte r factor should be considered, but gaseous radiationma y be neglected unde r ordina ry condition of flue gas meas-urement.

* David, Phi2. M a g . , 25, 256 (1913); P ro c . Roy. S O L . London), SEA,

4 Von Helmholtz and Julius, “Die Licht und Warmestrahlung ver-

6 Haslam, Lovell, and Hunneman, THISOURNAL, 17, 272 (1925).

183, 303 (1920-1).

brannten Gas&,”Beiblatter W i e d e m a n , 14, 602 (1890).

EXPRESSIOKF ERRORS -4PERCENT-TOllow the com-parison of the accuracies obtained by various methods of meas-urem ent of gas tem pera tures used under widely differentconditions, the following concept of “per cent erro r” is sug-gested. A measurement without error gives the true gastemperature, while a measurement that has the maximumpossible error due to ra diation will actually indicate the wall

tempe rature. These are the two extreme readings and anordinary measurement of a gas temp erature m ay be anywherebetween. Th e error in the reading will be expressed as a percent of the m aximum possible error; tha t is, the per ceni erroris obtained by taking the difference between the true and th eindicated gas tem pera ture a s a per cent of the difference be-tween the true gas temperature and the wall temperature.

Sugges ted Methods of M e a s u r e m e n t

or thermom eter tends to reach (1) he true gas temperature byconduction, and (2 ) the wall temperature by radiat ion.The relative effect of these facto rs determines the tem peratu reindicated by a thermocouple. It is therefore possible to mak ethe reading approach the true gas temperature by making

radiation less influential. A polished metallic surface maygive off or abso rb less th an o ne-tenth of th e radia tion of a noxidized or smoky one. For this reason a bright silver coveron a thermom eter greatly decreases the influence of radiation.

REFLECTING HERMOMETERURFSCE--k thermocouple

fXTRAPOLATlON METHOD O f

OBTAINING TRUt GAS Tft lPCRATURE

(Kreisinqer and Barlley)

Moss Velocrfy of cpses about 0.3 ounds

per ~econdper q. t.

FI G. 1

I800

400

0 0.1 0.2 0.3 0.4 0.3

More than a century ago an English doctor, W. C. Wells,Ecompared the readings in the atmosp here of a bare thermom-eter and one covered with gilt paper, finding a difference of6 ” to 12’ E‘. Mottelson’ suspended a bare thermometer andone covered with a polished silver shield in the air above a

6 “Essay on Dew,” 1814.

7 M. I. T. hesis, 1921.

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40-1 IXDUSTRI AL AND ENGTNEERIA’G CH E MI STR Y Vol. 17 , No . 4

red-hot furnace. The average reading of the bare thermom-eter was 502’ F., while th at of t he silver-shielded one was 320’F. RobinsonM roposed calculating the true gas tem pera turefrom the simultaneous readings of a gilt and blackened ther-mometer. This calculation gave a true gas tem peratu re of268” F. for the experiment of Mottelson. An accurateknowle dge of t he tw o black b od y coefficients an d of th e coeffi-

cient of he at tran sfer to the couple are required for this calcu-lation. The black body coefficients are not accurately known,however, which makes this calculation unc ertain . On accountof tarnishing, it is not practical t o use such shields at hightemperatures or in corrosive gases.

Figure 11-High Velocity Thermocouple

SMALLOUPLE-h increase in rat e of heat transfer byconduction will also bring the therm ometer or pyrom eter closerto the true gas tempe rature. This ma y be accomplished, forexample, by using a smaller thermocouple, since the rate ofconduction of heat per un it area is greate r for a small wirein a gas than for a large one, while the heat transferred byradiation is proportional to the surface. Kreisinger andBarkleyg placed a large an d a sm all thermocouple side byside in a boiler setting. Th e fine couple indicated a muc hhigher tem perature t ha n the large one, as shown in Table 11.

Table I1Postition A Position M

F. F.Couple diameter 0.008 inch 1780 1670Couple diameter 0,450 nch 1550 1270Difference in t emperatu re 230 400

EXTRAPOLATIONO READING T Z E R O DIAMETER-Kreis-inger and Barkley assumed that a couple of infinitely smalldiame ter would read the tru e gas temp erature, reasoning tha ta high rate of h eat transfer by conduction would make theeffect of radi ation negligible. Fro m a plot of the simultane-ous readin gs of a clus ter of coup les of diam ete r 0.5 o 0.01 nch,they extrapolated t o the reading corresponding to a couple ofzero diame ter. Thi s extrapolation is illustrated in Figure I.Although the slope of th e curve is changing quite rap idly a tthe small diameters, the extrapolation appears to give rea-sonably accura te results. Th e shape of the curve dependsupon the gas velocity and the temperature of surroundingsurfaces. This interesting method seems to require furtherstudy, for example, to determine the effect of differences inblack bo dy coefficient upo n the s hap e of the curves.

RADIATIONmEms-Where the surfaces which the couple“sees” are a t the true gas tempe rature, the radiation error is,of course, eliminated. If the thermocouple is surrounded bynonconducting surfaces such as insulating bricks swept by thegas strea m, this condition will be very nearly realized. Shieldsof this nature may be set up to protect a thermocouple fromradia tion effects. Th e Bu reau of Mineslo has used a clay lin-ing in a gas-sampling hood and measured flue gas tempera-

8 THIS OURNAL. 13,820(1921)

9 Bur. M i n e s , B u ll 145 (1918)

10 ~ t r i ~s, 32 (1912). 7, 48 (191.5)

tures therein. They assumed th at the true temp eratures wereread . Th e accuracy of this assumption depends upon howclosely to th e tru e gas tempe ratures the surface of such ashield would be heated. Experim ents described later in-dica te tha t with gas velocities of a bove 20 feet per second a

couple in such a shield should give quite accurate readings.HIGH-VELOCITYHERM OCOU PLE-A etho d of mea suring

gas temperatures has been developed at MassachusettsInstitute of Technology, which simultaneously decreases theeffect of ra diatio n and increases the r at e of hea t transfer byconduction. A small thermocouple is surrounded by a quar tzor porcelain tube, as indicated in Figure 11. The coupleand surrounding tube are inser ted in the gas s tream whosetempe rature is to be measured a nd a rapid stream of gasis drawn o ut through th e tub e by suction. The high veloc-ity increases the rate of conduction an d both the inn er sur-face of the tub e an d the thermocouple t ip rapidly approachthe gas tempe rature. Since the tip is surrounded by surfacesat practically the true gas temperature, the radiation correc-tion is negligible. Mea sureme nts ma y thus be made inde-penden t of both t he tem pera ture of the surroundings and thevelocity of the gas s tream.

Forrest” compared the readings obtained from such a high-velocity tub e with those of a bare thermocouple. Th e high-velocity tub e extended to th e center of a 6-inch she et ironflue leading from a gas furnace, t he b are couple being exposedalongside. Forrest assumed that the high-velocity tub e wasreading the t rue gas tempera ture, an assumption which seemsjustified by the observation th at the reading was not depend-ent upon the gas velocity within th e tub e so long as it was keptabove a definite minimum; th at is, as the suction was in-creased the reading of th e high-velocity therm ocouple rose to amaximum and a ny furthe r increase in gas velocity by increasedsuction caused no change in the indicated temperature. Alarge difference was observed between th e reading of the high-velocity thermocouple and that of the bare couple placed

500 WO 700 WO 900 1000 11W it00 1300 1400 1500 1bOO ‘f

Read is of Hb h Yelocif_y Thermocouple

FIG. III

alongside. Th is difference was great when the bare couple waslarge and at high temperatures. Th e da ta of these experi-men ts are given in Figure 111. Conditions were not carefullycontrolled, but these data indicate the great er rors in thereading of a bare couple under such conditions. Assumingthe true gas temperature to be shown by the high-velocitytube, and measuring the pipe or wall temperature with athermocouple, Forrest calculated values of h , for the variouscouples using E quati on 3 above. These values are plotted in

11 Special Report, M . I . T., Chemical Engineering Dept., 1988.

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April, I925 I S C;S TRI-4L A S I ) E S G I .VEERI S G CHE.IIIST R I.’ 405

Figure IT’.

and Elliot.”given in Table 111.

Similar experiments were reported by LehnhardtSpecimen data taken from their report are

Table 111-Experiments with High-Velocity Thermocouple

Temperatures in ‘ . Ah s . ( = F. + 480)

Wall tem- Tempera-Flue gas perature ture of cou-

velocity (thermo- Tempera- ple in high-Lbs. ’wr./ couple meas- ture of velocity Error of511 ft . urement) bare couple tube hare couple

I TU T C T T - T c

Apparentcoefficient

of heattransfer to

hare cou-pleil c

0 , 0 8 3 86 0 1295 1352 8 i 3 7 . 40 . 1 , j i 916 1476 153s d9 7 7 . 00 171 961 1 5 7 4 1747 l i 3 3 2 . 90 171 96O 1596 1737 141 4 2 . 9

The coefficients as calculated do not agree well amongthemselves, How ever, these experiments illustrat e the ap-plication of the high velocity thermocouple and indicate theincreased accuracy of its measurements. It may be noted tha tthe co efficients of h eat t rans fer to th e bare couple, h, , as cal-culated both by Leh nhard t and Elliot and by Forrest, are muchlarger than those which have been directly determined forcylinders of the d iame ters of the couples tha t the y used.This is probably due to their assumption tha t the tempera-tur e of th e surfaces radia ting to th e couple can be measured bya thermocouple on the pipe wall (and also lack of knowledgeof black bod y coefficients, etc.). These effects are discussedlater. However, the very rapid decrease in temp erature differ-ence with decrease of couple size as found by Forre st (Figu re111)illust rates the increase of accuracy gained by th e use of avery small thermocouple. Th e entire series of results indicatesthat an accurate reading of a gas temperature may be ob-tained with the high-velocity thermocouple.

Experiments with Factors Controlled

G E N E RA LROCEDURE-The inv estigat ion s ju st desc ribedwere carried o ut u nde r more or less accidental conditions, an dit w as tho ugh t desirable to examine the behavior of thermo-couples und er conditions app roach ing those of act ual practice,and yet with the gas temperature, wall temperature, and gasvelocity indepen dently known. This investigation’* was

TO BARE COUPLE5 OF YARIOUS 51ZE5

H g h Velocify Thermocouple Fgn

,I 1 I 1 hmpora tureol Ga,(HighVcla,tyThermoMvple) 1 1400 600 m a iwo 1 2 ~ 14w 1606 F.

fs . p

intended to in dicate the conditions under which it is practica-ble to calculate a correction using Equation 3 arid the con-ditions under which it is better to prevent the radiationcorrection by shields or high velocity tubes .

It was necessary t o know the actual te mpe rature of the gaswith which the thermocouple was in contact. This was diffi-cult because of th e rapid change of gas tem per atu re while pass-ing over walls at a different temperature. Th e procedure

** Chappell, “True Measurement of High Gas Temperatures,” M I. T.

Thesis, 1994.

adopted was (1) t o measure the true temperature of it ga sstream, keeping the walls at the same temperature as thegas, thus eliminating an y correction for radiation; (2 ) to passthis gas through a sh ort length of pipe at a greatly differentwall temperature, placing the test thermocouple at the mid-point of this pipe length; (3) to measure a second true gastemperature with radiation corrections eliminated as in (1).

The true temperature of the gas at the thermocouple couldbe satisfactorily calculated from (1) and (3) by interpolation.

WALLAT RED HEAT -The apparatus used is diagrammedin Figure V. A blower delivered air through a standardorificeI3 so that the volume was known to within 3 per cent.When a gas stream above room tem perature was desired thisair was passed through a surface combustion furnace andburned with illuminating gas on hot brick. The gas from thefurnace was passed thro ug h a series of right-angled bend smade up from standard 2-inch iron elbows and nipples.Thi s baffle pipe was placed in a wooden box an d insulated onall sides by about 6 inches of Sil-o-C el flour (B ox I and 11,

Figure V). Electric heating wire in the packing materialsupplied the heat losses from the surface of the box. The r-mocouples were imbedded in the metal near the two ends ofthis baffle pipe (1 and 3, Figure V ), while at the center of th ebaffle pipe a couple was exposed in t he gas stream (2 ,Figure V) .When th e electric heaters had brou ght th e end couples in th emetal to the temperature of the middle couple in the gasstream, th e lat ter thermocouple gave the true gas temperaturewith radiatio n errors eliminated. Th is gas stream of knowntemperature was the n passed through a 9-inch length of stand-ard 1-inch pipe kept at a uniform red heat by a surroundingfurnace. From nea r the ends of this 9-inch length, tubesextended to th e outside of th e furnace, the out er ends beingcovered with mica windows. Throug h these windows andtube s the inn er surface of th e hot pipe was visible and itstemp erature was measured to within ab out 5 degrees by a h otmire optical pyrometer. Th e true temperature of the gasleaving this hot tube was measured in a second baffle box.

Th e test thermocouple mas exposed a t the midpoint of t hehot tube. The couple leads were No. 22 chrome1 and alumelwire and were brought out through the furnace in a water-cooled tube. Th e tips were spherical, the larger ones beingof iron. Th e da ta in Table IV illustrate the readings made.

WALLS ELOW R E DHE AT -TO investigate t he case of a hotgas an d cold walls presented more difficulties. Th e tempera-ture of the inner or radi ating surfaces of th e malls could notbe measured directly by rad iation or optical methods. How-ever, it seemed interesting to know w hat results would be ob-tained by measuring the wall temperature with a thermocoupleand using this as an inner surface rad iating temp erature.

Walker, Lewis, and hZcAdams, “Principles of Chemical Engineering,”

p. 53 .

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5a

e-l d

Vol. 17, No. 4

I I I I I I

COEFFICIENTOFHEAT TRANJFCR

. TO THERMOCOUPLE3

Table IV-Experiments with Cold Gas Passing over Couple Placed in Ho t Tube

(Temperatures in ‘ . Abs.)

of gas First true tern- Temperature temperature ture gas at cou- temperature “Error” of bare Error as per heat transferass velocity Second true True tempera- Apparent gas Coefficientof

Lbs./sec./sq. f t. perature of gas of walls of gas ple in hot tube (couple reading) couple difference cent of to coupleV TI T w Ta TO TC T o - To T w - To h e

Diameter of couple. D = 0.07 i n c h

0.000 . 3 80 . 4 70 . 7 0

1 . 0 71 .5 72 . 4 4

0 . 4 30 . 5 50 . 7 51 .1 91 . 6 82 . 6 4

526540540’

540540540

540540540540540540

184018871853188018801830

S i6893870860821810

746716705700680675

19191268124111781100988908

Diameter of couple. D = 0.31 in ch

97892589287 4845812

Veiocib’v’ in Poun&/Jec./&, Ft.

FIG, PI

Consideration of th e dat a of Tab le IV shows th at th etemperature difference between pipe an d gas was practicallycons tant for t he whole leng th of pipe, so th at th e rate of changeof temperature was very nearly uniform and the true tem-perature of t he gas at the midpoint, T,, was within 2 or 3per cent of the arithmetic mean of TI nd Tf. The tem-perat ure of the wall, T,, was read directly by an opticalpyrometer.

Considering these da ta as illustrating the behavior of ther -mocouples under similar conditions in practice, we may es-timate the percentage error in the readings of such thermo-couples. Th is error is expressed in Table IV as a per cent ofthe total difference in temperature between gas and sur-

roundings.

759733716706694676

13831340122611821067938

536525471398306234

622606509475372261

. .474639332519

56534 5403422

1 9 : i2 0 .32 5 . 53 0 . 23 9 . 65 6 .1

1 3 . 11 6 .31 9 . 82 3 . 5 .3 1 .641 .9

CALCULATION OF TRUEGAS EMPERATURE-The da ta ofTable IV show that the difference in temperature betweencouple reading and true gas temperature varies with thegas velocity, couple diameter, wall temp eratur e, etc. Theseda ta m ay be compared b y calculating the coefficient of heattransfer, h,, between gas and couple from Equation 3, sub-stituti ng the experimentally known factors. From consid-

eration of the data available (Table VII) the black bodycoefficient for th e couple was tak en as 0.64. Figure VI givescalculated values of h , plotted against mass velocity. Itis seen that this coefficient directly depends upon the gasvelocity and the couple diameter, so that f rom the princi-ple of Equation 3 the true gas temperature could be cal-culated from the couple reading, the wall temperature,the gas velocity, and the couple diameter, since the coeffi-cient of he at transfer t o th e couple is a function of t he tw olatt er factors. This calculation is useful both as a directmethod of obtaining true gas temperatures and as a means ofestimating the probable errors in reported measurementswhere th e conditions were not carefully controlled.

A satisfactory calculation of t he true gas temp eratu re isnot practicable under all conditions, as will now be shownby a consideration of the experiments described above us-in g a gas flowing within cold walls.

In series of experiments with hot tubes (Table IV) th e walltemperature or temperature of the surfaces radiating tothe couple was directly measured by a radiation (optical)pyrometer. However, a surface temperature below a redheat cannot be so measured and a pipe wall temperaturemu st be measured by a thermocouple. Th e data of Ta-ble V gives the wall temperature, T,,measured on th e outersurfa ce of th e iron pipe. Because of a small temp eraturedifference between pipe an d gas an d a longer length of pipewith greater change of gas temperature, the m idpoint tem-perature, Tm, as not the arithmetic mean of T i and T2.Assuming that the rate of heat transfer was proportionalto th e temperature difference and t o the sq uare root of theabsolute gas temperature, the following equation was de-

rived :

Th e true gas temperatures a t the thermocouple, Tm, erecalculated using E quation 4 nd are given in Table V. Thistable shows th at the difference between the tru e gas tem-perature and the indicated temperature or couple reading(Tm ,) decreases very rapidly bu t irregularly with increasedvelocity of gas through the tube. Thi s change may alsobe expressed in th e rapid increase of th e appar ent coeffi-cient of h ea t transfer between cou ple an d gas calculatedfrom the da ta of T able V, using Equation 3. These coeffi-cients are plotted against mass velocity in Figure V II.

Th e data of Tab le V or Figure V I1 show that when the

gas velocity through tube reached about20

feet per sec-

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April, 1925 I N D U S T R I A L A N D E N G I N E ER I N G C H E M I S TR Y 407

Table V-Gas Passing over Couple Placed in Tube below Red Heat

(Temperatures in O F. Abs.)

Mass velocity Secon d true Tru e tempera- Apparent gas "Error" ofCouple diameter of gas First true tern- Temperature temperature ture gas at cou- temperature bare couple

Inch Lbs./se c./sq.ft . perature of gas of bath of gas ple in hot tube (couple reading) differenceD v T I T u TI To TG Tc- To

0 . 0 80 . 3 00 . 3 00 . 3 00 . 3 00 . 3 00 . 3 00 . 3 00 . 3 00 . 3 00 . 0 8' 0 . 3 00.080 . 3 00 . 3 00 . 3 00 . 3 0

0 . 0 00 .4 10 . 6 10 . 7 20 . 9 31 .0 11 . 0 41 . 3 31 . 3 91 . 4 81 . 6 01 . 6 51 . 9 42 . 0 32 . 1 22 . 3 22 . 3 2

17301598142514351761163712481606165316611732169320501684164417091233

57673971071067 2

95567 281185 5

10101193

672135278277 3679672

10551032949949

1018

1148891

105111221176141410501524109411071089931

ond, the apparent coefficient of heat transfer between cou-ple and gas had become so large that the radiation correc-tion was negligible, even when the walls were apparentlyhun dreds of degrees colder th an the gas. Now the actua lcoefficient of hea t tran sfer between couple and gas is know nnot to increase so rapidly w ith velocity, and some factorin the calculation fwm which the coefficient was obtainedmust be in error. Th e calculated true gas temp erature mus tbe too high rathe r th an too low, since a g reater rate of hea ttransfer would be expected in the hot bends.

PAPARE N 7

600

800THERMOCOUPL E

V E L O C I T Y ~=PoVNDS/SEC./SG'. fT.

Consideration indicates that a false wall ternperaturewas being used in Equation 3 for calculating the coefficient

of heat transfer. Th e radiation which comes to the cou-

iiio111411141260

130810131234130313301533126816771298129812891031

5761070100810241202

122010131208126912841487124616501293129812741048

1461069058

8 80

264446462227

50

15- 7

Coefficient ofheat transfer

to couplehe

9171 0 . 41 2 . 45 1 .0

2 3 . 7

9 i : 76 6 . 85 4 . 58 9 . 0

149.239.660.

24f:

ple depends only upon the inner surface radiating tempera-ture of th e pipes, and app arently this was many hundreddegrees hotter than the metal temperature, which was meas-ured and used as T,. That is , i t seems th at much of thesurface of the slight layer of scale an d soot on t he insideof the pipe was heated to a temperature very close to thatof the gas and radiated to th e couple in proportion to thefourth power of this temperature, thus bringing the couplenearly to gas temperature. This explanation is supportedby several observations. Th e inside of th e pipes was foundto be coated by oxide scale 0.01 to 0.05 inch thick and withsoot to a depth of 0.003 to 0.02 inch. The conductivityof lam pbla ck in English unit s is 0.015, so th at a layer ofcarbon 0.012 inch or 0.001 foot thick would have a con-ductivity of only 0.015/0.001 = 15 . The over-all coeffi-cients of heat transfer between bath and gas through thepipe were between 5 and 20 for these experiments, so t h a tmuch of the tem perature dro p would have tak en place inthis film had i t been evenly distributed. However, sucha surface really consists of patc hes and points. Whenthese grow hotter than the su rrounding surface, the fourthpower law makes their radiation dominant for the entire

surface, small portions of surface at a high te mp erat uregiving off much more radiation than much larger portionsa t a slightly lower temperature. T ha t these particles maybe at practically gas temperature was shown in the caseof th e red-hot tub e whose inne r surface became splotchedwith black patc hes of cold scale, which dark ened as the gasvelocity through the tu be was increased. To show thebehavior of particles on the tu be surface, a bare, clean metalthermocouple tip was pulled hard against the inner surfaceof the cold pipe wall. Th e readings obtained ar e given inTable VI.

Table VIMass velocitv of eas 2. 55 lbs./sec./sa.ft.

.

Temperaturg of g al lTempe ratur e of gasTemperature of ouple against wall

672' F . Abs.1060' F. Abs.

995' F. Abs.

It is seen that the thermocouple tip, although restingagain st the surface of a colder pipe, was heated n early togas temperature. Conduction w as evidently low betweentip and pipe. This indicates tha t a carbon particle whichconducts heat much less than a metal thermocouple wouldtake up n early the true gas temperature even when restingon the pipe wall.

We may conclude from these experiments that (1) it isnot practicable to use a wall temperature as measured bya thermocouple fo r the calculation of a radiation correc-tion, especially at high gas velocities; (2) a thermocouplesurrounded by even slightly nonconducting surfaces readsvery close to the t rue gas temperature a t gas velocities above20 feet per second; (3 ) the high velocity tube method shouldgive very acc urate gas tem peratu res, as it artificially sur-

rounds the couple by surfaces at th e gas temperature.

8/2/2019 ie50184a024


408 I N D U S T R I A L ALVDENGINEERING C H E J I I S T R Y

Table VIII-Methods of T r u e M e a s u r e m e nt of G a s T e m p e r a t u r e s

Vol. 17 , No. 4

PRINCIPLE

Reduction of effect of radiation

Increase of ef fect of condu ction

Calculation

a Error in reading taken as:

Mass velocityof ga s

Lbs./sec./sq. ft.

Very low freeconvection

0 . 3 3

0 . 41 . 7

2 . 4 4

METHOD ADVANTAGES

Polished metal shield on couple Simple (11

(2)

Nonconduc ting radiation shields Simple (1)

Permanent (2)

Very small couple Simple (1)(2)

High-velocity thermocoup le Accurate with any gas velocity (1)

Extrapol ation to reading of cou- Simple calculation (1)ple of zero diameters (2)

Calculation from equilibrium Usable with ordinary data (1)

(3)(Gas temperature) - couple temperatu re)

(Gas temperature) - wall temperature) ' O 0 *

about couple

equation (2 1

DISADVANTAGES

Can only reduce errora of a couple to 1/10 (see

TarnishesTable VII)

Gas velocity must be over about 10 feet per

Sometimes difficult o instalsecond

Smallest practical sizes give appreciable r r ro rFragile and corrode

Requires suction

Per cent err or not yet establishedSmall couples fragile

Must know wall temperatureMust know gas velocityBlack body coefficients uncertain

Table IX-Approximate Errors in Methods of G a s T e m p e r a t ur e M e a s u r e m en t

(Temperatures in O F. )Calcd. by ex-

Temperature True tempera- Ordinary cou- Reading silver Reading very Reading "high- trapolation to Calcd. fromof walls tu re of gas ple reading shielded couple small couple velocity couple" reading a t zero equilibrium

T W TO TC Tc TC To diameter, T O equation, T C

1/4 of walls a t 268 502 error 80% 320 error 18%1400

1300 1840 (? ) 1560 error 54%

1380 300 920 error 56 %500 1277 (? ) 1136 error 18%

1780 error 11 % 1'860evor4% 1824 error 3%

228 error 6%

1277 error zero (? )

I444 350 448 error 9% 340 error 1%

. . . . . . . . . . . . . . .

S u m m a r y of Method of Calculation of True GasTemperature

The equation for the equilibrium governing a gas tem-perature measurement is in English units:

h , ( T o - T u ) = p 0.162 [ (G) '- (3'1where T, = tru e gas temperature,. O FdAbs. (= O F,+ 460)

T , = observed couple reading, F. Abs.T m = temperatures of surrounding surfaces, O F. Abs.

p = black body coefficient of couple

h , = coefficient of heat transfer from gas to coupleIt is assumed that surfaces at a temperature T, entirelysurround the couple. A correction can be made fo r thesolid angle subtended by an y cold bodies. Th e black bodycoefficient is th at of th e couple and depends upon i ts ma-terial and temperature. There is much disagreement in theliteratu re as to these coefficients and a t horo ugh investi-gation of this imp ortant sub ject is desirable. However,the data in Table VII, taken from the Smithsonian Tablesof 1919, may be used fo r the estimation of p .

T a b l e V I1MATERIAL Black body coefficient

Polished silverPolished platinumOxidized aluminiumOxidized nickelOxidized monelOxidized copperOxidized cast ironOxidized steel

0 . 0 20 .080 .1 10 . 3 70.410 .5 70 . 6 40 . 7 9

The coefficient of heat transfer to the couple, he , dependsupon fact ors which may be grouped for convenience-as size of couple, gas velocity, an d tem per atu re of gas andcouple. T he coefficient depends upon th e molecular prop-erties of the gas, but most gases met with in practice (fluegas, producer gas, etc.) resemble air very closely an d a com-mon equation may be used. From several sources, datafor the transfer of heat between air and a transverse cylin-der h ave been correlated,14 and ma y be conveniently ex-

14 McAdam s and Chappell, "The Coefficient of Heat Transfer between

8 Flowing Ga s and a Transverse Cylinder," unpublished article. Da ta

from the following: Hughes, Phil. Mag., 1, 118 (1916); King,Phil. Trans.,

214, a7 3 (1914); Kennelly, J . Am . Ins l . E l c r . Eng., 48 , 363(1909); Carrier,

Trans.Am SOC.Mrch. Eng., 89, 1055 (1911);Nusselt,Gcsundh. I ng . ,38,490

(1915); Chappell. M. I. T. Thesis, 1924.

pressed by the following equation:-e = 0.30 dT* (5)

where h , = coefficient of heat transfer, English unitsV = velocity, pounds/second/square foot free areaD = diameter, inches

T , = O F. Abs. mean temperature of gas and couple

If the temperature difference between couple and gas isnot great, it is sufficiently accurate to use the couple temper-

ature.The above equation is a simplified form of the following

general equation :

0 . 4 V 0 . 6 7 +0 . 0 P l o gD

0 0 . 5, = 0 51 T,,,

The data which this equation expresses are for diame-ters 0.001 to 2 inches, velocities 0.2 t o 5.0, and tempera-tures to 2260" F. Abs. (1800" F.). The temperature func-tion should hold in air to an y tempe rature which can be meaa-ured by a thermocouple.

The use of this method may be illustrated by calculatingthe true gas temperature fo r the experiment of line A , Fig-ure I, from the reading of one of the couples.

The data are: D = 0.31 inch

T , = 2030' F. Abs. (1570 O F.)V = 0.33 pound/second/square footTW = 1760' F.Abs.

A silica tube was used about the couple proper and wewill assume th at i ts black bo dy coefficient was 0.3. The accu-rate e stima tion of this facto r is difficult.

From Equation 5

From Equation 3

14 (T , - 2030) = 0.30 X 0.162T, = 2030 + 254 = 2284' F. Abs.Tu = 1824' F.

[(20.3)' - (17.6)'l

It will be noted th at th e method of extrapola tion gave

T , = 1860"F.

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